Science - USA (2020-03-20)

Ip¼

Vdc

4

1

Rp

þ

1

rp



xc

w

Vdc

2

1

Rp

1

rp



þ



ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Vm^2 Vdc^2

p

p^2

1

Rp

1

rp

 

ð 6 Þ

and the imaginary parts of half-cycle averaged
currents are

in¼i

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Vm^2 Vdc^2

p

p^2

1

Rn

1

rn



ð 7 Þ

ip¼i

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Vm^2 Vdc^2

p

p^2

1

Rp

1

rp



ð 8 Þ

The complex current is simply a result of
the complex admittance of the tunnel diode
I=(G+iB)V, whereGis the conductance,
Bis the capacitive part, andV=Vdc+V 0 (x)eiwt.
The self-consistent dc voltage can be esti-
mated by the current-matching condition,
which requires that the half-cycle currents
be equal and in opposite directions, such that
In=IpatVdc. For matched tunnel diodes,Rn=
Rpandrn=rp, the self-consistent dc bias is
Vdc=Vm. However, in general, these equations
lead to a transcendental equation for the self-
consistent dc bias voltage.
A key feature of the bipolar conversion de-
vice is the periodic buried pn junction under
the metal. The interdigitated nature of the
structure leads to essentially a periodic well
structure for storage of charge that can be
pumped by the combined action of the two
forward-biased tunnel junctions, metal to n+
and p+ to metal, respectively. We can extend
the analysis of grating-coupled diode array as a
simple (ideal) pn junction photovoltaic by con-
sidering the total device current across the pn
junction asI¼I 0 ðexpðbeVÞ 1 ÞIph, where
the photon-assisted tunnel current,Iph, acts
as a photocurrent in analogy with light ab-
sorption in the depletion region of the pn
junction. Here,IphisgivenbyEq.5or6,which
are equal at the self-consistent bias point.
The resulting open-circuit voltage across the
pn junction is

Voc¼

1

be

ln 1 þ

Iph

I 0



ð 9 Þ

Similarly, the short-circuit current isIsc=
−Iph. The open-circuit voltage across the pn
junction can far exceed the confined voltage
amplitude in the tunnel barrier, becauseVth¼
kT=e>>Vm(Fig. 2C). The larger the open-
circuit voltage, the greater the power genera-
tion in the bipolar device. This model implies
that the RC time constant of the pn junction is
such that it cannot respond to the infrared
(35-THz) input signal, and the device charges
across a nearly static depletion capacitance.

Experimental results

Electrical power generation from a moderate-

temperature source is measured using a vac-

uum TPV setup (Fig. 1A) with an ~2-mm gap

between sample and heat source, which has

been previously described ( 20 ). The bipolar

grating-coupled device active area is ~60mm

by 60mm, and the grating pitch is 3.0mm with

ametalwidthof1.8mm(Fig.2A).Thedeviceis

a three-terminal device with interdigitated n

and p regions with separate n, p, and metal

contacts. The induced voltage from the ther-

mal source at fixed temperature is measured

by shorting the pn junctions with a variable

load resistor and measuring the induced volt-

age as a function of the load resistance with a

nanovoltmeter (Fig. 3A).

The process and device parameters play a

key role in the performance of the bipolar

device. The oxide thickness and composition

affect the tunneling resistance and the ENZ

field concentration, respectively. Moreover,

the implant conditions and thermal anneal-

ing cycles greatly affect the pn junction char-

acteristics, such as resistance and depletion

width from dopant diffusion under the metal

1344 20 MARCH 2020•VOL 367 ISSUE 6484 SCIENCE

Fig. 3. Bipolar device power generation.(A)Circuit schematic of device contacts for power generation.

(B) TEM cross sections through a nominal 4-nm gate oxide stack (device 1) and through a nominal 3.5-nm

gate oxide stack (device 2). (C) Measured power density for device 1 as a function of the load resistance

for various source temperatures and measured voltage across pn junction shorted by a load resistor versus

load resistance for various source temperatures. (D) Measured power density for device 2 as a function

of the load resistance at fixed source temperature for grounded and floating metal gates and measured

voltage across pn junction shorted by a load resistor versus load resistance.

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